The Combinatorial Loewner Property and super-multiplicativity inequalities for symmetric self-similar metric spaces
Year: 2024
Type: preprint
Abstract: This paper introduces a general construction of self-similar metric spaces as limits of discrete graphs. Our framework produces many classical examples, such as the Sierpiński carpet and the higher dimensional Menger sponges, but also a rich class of new examples. The main result of the work roughly speaking states: If the construction is sufficiently symmetric then the limiting object supports useful moduli estimates, namely the Combinatorial Loewner property of Bourdon--Kleiner and the super-multiplicativity inequalities. The latter are established on Menger sponges for which it had not been previously known. The main new technique the work offers is a general framework of flows and resistance estimates.
Source: arXiv (Cornell University)
Authors: Anttila, Riku, Eriksson-Bique, Sylvester
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402705955